The present invention relates to an apparatus for optically analyzing wavefronts of light and forming two-dimensional images at some positions taken in the direction of the depth of a three-dimensional object, i.e., equidistant images on real-time basis, using phase conjugate waves.
In Applied Optics, Vol. 22, No. 2, pp. 215-232 published on Feb. 15, 1983, Nils Abramson reported that light wavefronts were recorded and recreated on a hologram, using coherent laser beam pulses of a quite short pulse duration.
FIG. 1(A) is a schematic diagram of an apparatus for recording light wavefronts by means of holography. Some of the light emitted from a laser L passes through a spatial filter A to an observed point C on an object O, and reflected therefrom to a point B on a hologram plate H to form object waves. Another portion of the light passes through the spatial filter A, mirrors E and D to the point B to form reference waves. The object waves and the reference waves interfere with each other. As a result interference fringes are formed on a recording surface that is, the hologram plate H, and then it is developed to complete pholography. If the laser beam produced by the laser L has a short coherence length or takes the form of short pulses, and an object O of interest is a whitepainted door having a reflecting matter (M) such as a mirror thereon as shown in FIG. 1(B), it is possible to record and recreate the light wavefronts themselves, unlike holograms.
Particularly, using the aforementioned light source, only those light rays which are passed through the points A, E, D, B and the points A, C and B respectively and which have the difference of their optical paths within the coherence length of the pulse duration interfere with each other on the surface H. Those light rays which differ in optical length over the coherence length of the pulse duration do not form interference fringes.
More specifically, object waves arriving at e.sub.o on the object o form interference fringes only at point h.sub.o on the surface H. Similarly, object waves arriving at e.sub.1 and e.sub.2 produce interference fringes only at h.sub.1 and h.sub.2, respectively. The hologram created in this way is developed and illuminated with only the reference waves, which are then diffracted by the interference fringes recorded in each portion on the hologram H. Thus, the light used to form the interference fringes is recreated. The observing point is moved along the surface H to observe time-variation of the light wavefronts as shown in FIG. 2. FIG. 2 is a diagram showing the photographs taken during the reconstruction of one single hologram plate. In FIG. 2, O and W represent an object door and a light reflected by a mirror on the object, respectively. As described above, a wavefront can be observed by combining an interference property of a laser light having a short coherence length or a short pulse width with a conventional holograph technique.
Furthermore, if the wavefront observing technique as described above is applied to a three-dimensional object observing technique for three-dimensionally observing an object, for example, plural equidistant images of the three-dimensional object can be observed. Such a technique for forming equidistant images that is, three-dimensional images from a three-dimensional object will be described in detail with reference to FIGS. 3, 4, 5 and 6.
It is generally known that two laser beams produced from a laser interfere with each other only if their optical paths are substantially the same. This principle is next described briefly in connection with a Michelson interferometer shown in FIG. 3.
Referring to FIG. 3, a laser 50 produces a laser beam P1 which is divided into a laser beam P2 and a second laser beam P3 by a half mirror 51. The beams P2 and P3 proceed to mirrors 52 and 53, respectively. The beam P2 is reflected by the mirror 52 and returns to the half mirror 51. Similarly, the beam P3 is reflected off the mirror 53 and goes back to the half mirror 51. The two laser beams P2 and P3 returning to the half mirror 51 form a composite light P4 which is then detected. Assuming that the mirrors 52 and 53 are spaced at the distances L1 and L2, respectively, from the half mirror 51. The difference in optical path between the laser beams P2 and P3 which is created in making one reciprocation is given by EQU .DELTA.l=2.times..vertline.L1-L2.vertline.
One laser beam lags the other by the amount given by EQU .tau.=.DELTA.l/C
where C is the light velocity.
Referring next to FIG. 4, the laser beam produced takes the form of a pulse having a given duration of .DELTA.t. If the time interval .tau. between the two laser beams P2 and P3 is larger than the duration .DELTA.t, then one of them reaches the half mirror 51 before or after the other arrives at the half mirror 51. At this time one beam cannot interfere with the other and so no interference is found in the composite light P4. In order to produce interference, the optical-path difference .DELTA.l between the laser beams P2 and P3 must be less than C.DELTA.t. Where the laser beam takes the form of short pulses, the duration .DELTA.t is quite short, and therefore, interference takes place only when the optical-path difference .DELTA.l is quite small. The maximum possible value of .DELTA.l, i.e., C.DELTA.t, at which interference occurs is known as the coherence length. In other words, shorter laser beam pulses have shorter coherence lengths.
FIG. 5 shows an apparatus for forming equidistance images from a three-dimensional object, for example, a propeller as shown in FIG. 5, using the shorter laser beam pulses an described above. This apparatus includes a laser 61 for producing an object beam toward a three-dimensional object, for example, the propeller 60 of a blower as well as a reference beam, a photographic dry plate 62 for recording the interference fringes of the object beam reflected by the propeller 60 and the reference beam, and two mirrors 63 and 64 for guiding the reference beam from the laser 61 to the plate 62.
The laser beam from the laser 61 is caused to extend over an angle of .theta.. One portion of it is incident to the propeller 60 as an object beam, while the remaining portion is incident upon the mirror 63 as a reference beam. The object beam incident upon the propeller 60 is reflected by the propeller and reaches the dry plate 62. The reference beam incident upon the mirror 63 travels to the dry plate 62 through the mirrors 63 and 64.
Interference fringes are produced on the photographic plate 62 in this way only when the difference in optical path between the object beam and the reference beam is less than the coherence length determined by the duration of the laser beam.
In the structure shown in FIG. 5 the reference beam reaches at a recording position H1 on the plate 62 after traveling the shortest optical length. Therefore, the beam which interferes with this reference beam is limited to the object beam traveling from a position S1 taken in the direction of the depth of the propeller. Likewise, the beams that interfere with the reference beams arriving recording positions H2 and H3 on the photographic dry plate 62 are restricted to the object beams traveling from positions S2 and S3 taken in the direction of the depth of the propeller 60. In this way, interference fringes which are formed by the interference of the reference beam with the object beams traveling from the positions S1, S2, S3 are recorded at positions H1, H2, H3, respectively, on the photographic plate 62.
The interference fringes recorded at the positions H1, H2, H3 on the photographic plate 62 are developed to create a hologram. When this hologram is illuminated with only the reference beam, only the object beams reflected from the positions S1, S2, S3 are recreated from the recording positions H1, H2, H3 on the interference fringes. Consequently, it is possible at a position B1 to observe an image formed by the object light traveling from the position S1. The images based upon the object beams originating from the positions S2 and S3 taken in the direction of the depth of the propeller 60 can be successively observed by shifting the position at which the observation is made to positions B2 and B3 one after another.
FIGS. 6(A) and 6(B) show images of the propeller 60 recreated by installing a camera (not shown) at observational positions B1 and B2, respectively, and taking pictures. As can be seen from these figures, equidistant images at the position S1 can be observed as recreated images at the observational position B1. Equidistant images at the position S3 can be observed as reconstructed images at the position B3.
The conventional apparatus as described above utilizes a holography technique, so that the interference fringes recorded on the photographic plate 62 must be developed to create holograms. Further, the holograms must be illuminated again with the reference beam to recreate images. Thus a considerable amount of labor is needed to observe a wavefront and equidistant images with a wavefront observing technique and it is impossible to observe the wavefront and the equidistant images on a real-time basis.